The Working Group has examined recent recommendations for evaluating and expressing uncertainty in measurement [Guide to the Expression of Uncertainty in Measurement, International Organization for Standardization (ISO, 1993)]. The present publication updates an earlier report of the IUCr Subcommittee on Statistical Descriptors [Schwarzenbach, Abrahams, Flack, Gonschorek, Hahn, Huml, Marsh, Prince, Robertson, Rollett & Wilson, (1989). Acta Cryst. A45, 63-75]. This new report presents the concepts of standard uncertainty, of combined standard uncertainty, and of type A and type B evaluations of standard uncertainties. It expands the earlier dictionary of statistical terms, recommends replacement of the term estimated standard deviation (e.s.d.) by standard uncertainty (s.u.) or by combined standard uncertainty (c.s.u.) in statements of the statistical uncertainties of data and results, and requests a complete description of the experimental and computational procedures used to obtain all results submitted to IUCr publications.